In the current paradigm of star formation, the densest regions of giant molecular clouds collapse into clumps, which eventually form Young Massive Clusters (YMC) which removes the molecular gas in its surrounding, decimating further star formation. Surprisingly there is cold molecular material very near (<10pc in projection) R136, the nearest YMC, located in the 30 Doradus star forming region in the metal-poor (0.5 Zo) LMC. According to most theoretical predictions, the photo-ionizing luminosity of the cluster is sufficient to evacuate any dense molecular gas surrounding the cluster within ~1 Myr. We present high spatial resolution ALMA maps in CO(3-2) that resolve the spatial structure of the cold gas. We determine their velocity distribution and the density of the molecular gas near R136 from the high density tracer CS(7-6) map and derive the molecular cloud properties in this extreme environment. We explore the origin of this weak cold CO gas and analyze if these represent molecular clumps (gas mass ~ 10^3 Mo) driven by the outwards wind momentum or VERY DENSE clumps that have survived photo-dissocia